I may need to replace the furnace; I really don't know why because it's 'only' 21 years old. Anyway, it's always worked fine but on this trip, it only lights when electricity is available. Unplugged...
Sounds more like a battery problem. 12VDC voltage is too low for the furnace to light when the converter (powered by 120VAC from shore power or generator) isn't feeding the battery.